The Theory of the Pitot and Venturi Tubes, Part 2 Page: 7 of 10
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AERONAUTICS.
and justifies us in going on to find a closer approximation by treating
the gas as ideal and thereby using an approximation to the com-
pressibility.
Assuming, then, that equation (11) is applicable to the imaginary
current tube now under discussion, we have, by setting S-= 0, the
equation
= - P - 1 (15)
- ,k -1-
If we now set = 1+A and -=n we have
P /
) k-1 n---1 (n-1) (n-2)
-1=nad 1 + A-- n+ w+a etc.
P 2 1.2.3
Setting the I .... } = X2, substituting in equation (15), and noticing
that n A= P we have
k p
S= X 2 p-P(16)
which differs from equation (13), obtained by disregarding com-
pressibility, only in the correction factor
n -1 (n-1) (n-2) (n--1) (n-2)(-3) .
2 1-2.3 1-2.3-4
The quantity A= p-p' is the fractional rise of pressure at the
p
S mouth of the impact tube: hence it is, in practice, always a small
quantity. The value of k for gases is always between 4 and 1, so
.- :ok - 1
that n = is always between * and 0. Accordingly the terms of
X containing A are alternately negative and positive and when A is
small the series converges rapidly, the sum of all the terms in A being
nearly equal to the first term alone, so that if the first is negligible the
sum is negligible and X may be set equal to unity.
S The ratio of the specific heats of air is 1.40. Hence n= and we
have
o 10 95 1
1 49 686
; Aj t A A+etc. (18)
If an error of y per cent. in S is permissible, an error of y per cent. may
S = also be allowed in the correction factor X and the value of A may be,
5 y
at most, such as to make A= 100 or A= 0.056y. For any assigned
values of the error y percent. in the speed, the value of S can be
found from equation (13).107
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Buckingham, E. The Theory of the Pitot and Venturi Tubes, Part 2, report, 1989?; (https://digital.library.unt.edu/ark:/67531/metadc53589/m1/7/: accessed April 23, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.